A certain spectrum, indexed by a\in[0,\infty], of upper bounds P_a(X;x) on the tail probability P(X\geq x), with P_0(X;x)=P(X\geq x) and P_\infty(X;x) being the best possible exponential upper bound on P(X\geq x), is shown to be stable and monotonic in a, x, and X, where x is a real number and X...

Though there is a huge variety of different Tchebycheff-type inequalities in the literature a systematized structuring is missing. The few existing surveys remain rather enumerative. Therefore in this paper a structuring of Tchebycheff-type inequalities is suggested which is based on three...

The paper characterizes the class of weakly decomposable (aggregable) inequality measures which satisfy a new (weak) decomposition (and agregation) property. These measures can be decomposed into the sum of the usual within-group and a between-group term which is based on the inequality between...

The asymptotics of large deviation probabilities for two-sample non degenerate von Mises functionals and U- statistics of arbitrary degree is investigated. We find explicitly the main term of this asymptotics. Some examples motivated by nonparametric statistics are given. The result may be...

In this paper, we focus on and examine the empirical evidence of non- linearity in aggregate Canadian unemployment. Contrary to the conclusion reached in Murray et al. (1993), and using a corrected for bias simple non-parametric test (SNT), we reject the null hypothesis of a linear structure for...

We consider testing regression coefficients in high dimensional generalized linear models. By modifying a test statistic proposed by Goeman et al. (2011) for large but fixed dimensional settings, we propose a new test which is applicable for diverging dimension and is robust for a wide range of...

It is well known that the F-test breaks down completely when the dimension of covariates exceeds the sample size. This paper proposes a new test for part of regression coefficients in high dimensional linear models. Under the high dimensional null hypothesis and various scenarios of the...